Noise-induced phase transitions in field-dependent relaxational dynamics: The Gaussian ansatz

TL;DR

This paper develops an analytic mean field theory with a Gaussian ansatz to accurately describe noise-induced phase transitions and dynamical behaviors in spatially extended relaxational systems.

Contribution

It introduces a Gaussian ansatz-enhanced mean field approach that provides quantitative predictions for steady states, dynamics, and multistability in noise-driven phase transitions.

Findings

Quantitative results for steady state mean fields and distribution widths.

Analytic descriptions of dynamical approaches to steady or oscillatory states.

Prediction of initial-condition-dependent final states in multistable systems.

Abstract

We present an analytic mean field theory for relaxational dynamics in spatially extended systems that undergo purely noise-induced phase transitions to ordered states. The theory augments the usual mean field approach with a Gaussian ansatz that yields quantitatively accurate results for strong coupling. We obtain analytic results not only for steady state mean fields and distribution widths, but also for the dynamical approach to a steady state or to collective oscillatory behaviors in multi-field systems. Because the theory yields dynamical information, it can also predict the initial-condition-dependent final state (disordered state, steady or oscillatory ordered state) in multistable arrays.